At some point I stopped receiving messages sent via Contact Form, but they are listed under Feedbacks. The last time I received an email was February 12th. I'm guessing I upgraded Jetpack around that time (currently I am running 2.1.2).
Starting February 13th, I see messages listed under Feedbacks, but I was never emailed the messages. Everything worked fine prior to then, and I don't recall making any changes to my site around then (like installing new plugins or adjusting anything), so I'm pretty sure this has to do with upgrading Jetpack.
If any more information is needed, just let me know. Thanks!